Simulate 20 bernoulli trials with:

a success probability p = 0.75

p^{k}q^{n - k}

where p = success probability, q = 1 - p

Trial # | Success/Failure | Math Work 1 | Math Work 2 | Probability |
---|---|---|---|---|

1 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

2 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

3 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

4 | Failure | 0.75^{0}0.25^{(1 - 0)} | 1 x 0.25 | 0.25 |

5 | Failure | 0.75^{0}0.25^{(1 - 0)} | 1 x 0.25 | 0.25 |

6 | Failure | 0.75^{0}0.25^{(1 - 0)} | 1 x 0.25 | 0.25 |

7 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

8 | Failure | 0.75^{0}0.25^{(1 - 0)} | 1 x 0.25 | 0.25 |

9 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

10 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

11 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

12 | Failure | 0.75^{0}0.25^{(1 - 0)} | 1 x 0.25 | 0.25 |

13 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

14 | Failure | 0.75^{0}0.25^{(1 - 0)} | 1 x 0.25 | 0.25 |

15 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

16 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

17 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

18 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

19 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

20 | Success | 0.75^{1}0.25^{(1 - 1)} | 0.75 x 1 | 0.75 |

Given your success probability of 0.75:

we expect 0.75 x 20 = 15 successes

Our actual results were 14 successes and 6 failures

- If q > p, 0
- If q = p, 0.5
- If q < p, 1

Since q < p, 0.25 < 0.75, then our median is 1

Variance σ^{2} = pq or p(1 - p)

Variance σ^{2} = (0.75)(0.25)

Variance σ^{2} = **0.1875**

Skewness = | q - p |

√pq |

Skewness = | 0.25 - 0.75 |

√(0.75)(0.25) |

Skewness = | -0.5 |

√0.1875 |

Skewness = | -0.5 |

0.43301270189222 |

Skewness = **-1.1547005383793**

Kurtosis = | 1 - 6pq |

√pq |

Kurtosis = | 1 - 6(0.75)(0.25) |

(0.75)(0.25) |

Kurtosis = | 1 - 6(0.1875) |

0.1875 |

Kurtosis = | 1 - 1.125 |

0.1875 |

Kurtosis = | -0.125 |

0.1875 |

Kurtosis = **-0.66666666666667**

Entropy = -qLn(q) - pLn(p)

Entropy = -(0.25)Ln(0.25) - 0.75Ln(0.75)

Entropy = -(0.25)(-1.3862943611199) - 0.75(-0.28768207245178)

Entropy = -(-0.34657359027997) - -0.21576155433884

Entropy = **-0.034238445661164**

Probability = 0.75

Median = 1

Variance = 0.1875

Skewness = -1.1547005383793

Kurtosis = -0.66666666666667

Entropy = -0.034238445661164

Median = 1

Variance = 0.1875

Skewness = -1.1547005383793

Kurtosis = -0.66666666666667

Entropy = -0.034238445661164

Probability = 0.75

Median = 1

Variance = 0.1875

Skewness = -1.1547005383793

Kurtosis = -0.66666666666667

Entropy = -0.034238445661164

Median = 1

Variance = 0.1875

Skewness = -1.1547005383793

Kurtosis = -0.66666666666667

Entropy = -0.034238445661164

Free Bernoulli Trials Calculator - Given a success probability p and a number of trials (n), this will simulate Bernoulli Trials and offer analysis using the Bernoulli Distribution. Also calculates the skewness, kurtosis, and entropy

This calculator has 2 inputs.

This calculator has 2 inputs.

p^{k}q^{n - k}

p = success probability

q = 1 - p

For more math formulas, check out our Formula Dossier

p = success probability

q = 1 - p

For more math formulas, check out our Formula Dossier

- bernoulli trials
- Repeating an experiment using a bernoulli distribution
- expected value
- predicted value of a variable or event

E(X) = Σx_{I}· P(x) - kurtosis
- statistical measure describing the distribution, or skewness, of observed data around the mean. Also referred to as the volatility of volatility
- mean
- A statistical measurement also known as the average
- median
- the value separating the higher half from the lower half of a data sample,
- probability
- the likelihood of an event happening. This value is always between 0 and 1.

P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes - skewness
- measure of the asymmetry of the probability distribution of a real-valued random variable about its mean
- trial
- a single performance of well-defined experiment
- variance
- How far a set of random numbers are spead out from the mean

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